Elements of Point-Set Topology (Dover Books on Mathematics)
|Rating||:||4.55 (810 Votes)|
|Number of Pages||:||176 Pages|
Michael C Smith said An unusual, and unusually good, book on topology. Most books on topology start with topology on the Rn and then introduce the finer points of topology. Baum's book starts right out with abstract point-set topology without skipping a beat. I learned general topology from this book and I'd absolutely recommend this to any student and instructor, along with Counterexamples In Topology by Steen and Seebach.. "What you need to know" according to Bart E Snapp. I am currently a Math Graduate Student who is primarily interested in algebra. While I own several books on algebraic topology and algebraic geometry, I was for a long time without a point set topology reference. This book tells me concisely what I need to know - and is an excellent bargain!
Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. References have been supplied to suggest further reading to the interested student.. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level.To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics.After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spa